Question

Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non-conducting sphere of radius $R$ ?

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

The electric field intensity at a point lying outside the sphere (non-conducting) is
$E=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}$
where $r$ is the distance of that point from centre of sphere.
$\therefore E\propto \frac{1}{r^2}$ ..( i)
The electric fieid intensity at surface of sphere
$E=\frac{q}{4\pi {\epsilon }_0{R}^2}$
or $E\propto \frac{1}{R^2}$ ..( ii)
$R$, being the radius of sphere.
The eiectric field intensity at a point Iying inside the sphere is
$E=\frac{qr}{4\pi {\epsilon }_0{R}^3}$
or $E\propto r$ ..( iii)
Also at the centre of sphere $r=0$.
Hence, $E=0$. The graphical distribution is shown below